8x^2-30x+16=0

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Solution for 8x^2-30x+16=0 equation: 


Simplifying
8x2 + -30x + 16 = 0

Reorder the terms:
16 + -30x + 8x2 = 0

Solving
16 + -30x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -15x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -15x + 4x2)' equal to zero and attempt to solve:

Simplifying
8 + -15x + 4x2 = 0

Solving
8 + -15x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
2 + -3.75x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.75x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.75x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.75x + x2 = 0 + -2
-3.75x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.75x + x2 = -2

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = -2 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = -2 + 3.515625

Combine like terms: -2 + 3.515625 = 1.515625
3.515625 + -3.75x + x2 = 1.515625

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(x + -1.875) equal to 1.231107225 and -1.231107225.


Subproblem 1
x + -1.875 = 1.231107225

Simplifying
x + -1.875 = 1.231107225

Reorder the terms:
-1.875 + x = 1.231107225

Solving
-1.875 + x = 1.231107225

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = 1.231107225 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = 1.231107225 + 1.875
x = 1.231107225 + 1.875

Combine like terms: 1.231107225 + 1.875 = 3.106107225
x = 3.106107225

Simplifying
x = 3.106107225


Subproblem 2
x + -1.875 = -1.231107225

Simplifying
x + -1.875 = -1.231107225

Reorder the terms:
-1.875 + x = -1.231107225

Solving
-1.875 + x = -1.231107225

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = -1.231107225 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = -1.231107225 + 1.875
x = -1.231107225 + 1.875

Combine like terms: -1.231107225 + 1.875 = 0.643892775
x = 0.643892775

Simplifying
x = 0.643892775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.106107225, 0.643892775}
Solution
x = {3.106107225, 0.643892775}

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